Decreasing back EMF in motor due to increase in load Why does back EMF tend to decrease as the rate of doing work increases? When the load increases, it reduces the angular speed of motor and as a result, the induced current due to back EMF also decreases since the flux now changes at a slower rate than before.
Can we understand why this happens using a model of the physics?
 A: The typical DC motor architecture has dynamics governed by the equations $$\tau=k_\tau I,$$ $$\omega=\frac{V_E}{k_E},$$ $$V_{in}=IR+V_E=IR+k_E\omega,$$ obtained from the mechanical and empirical knowledge of the motor and the Kirchoff's voltage law where $\tau$, $0<k_\tau$, $\omega$, $V_E$, $0<k_E$, $0<R$, $V_{in}$ denote the motor torque, motor torque constant, motor angular velocity, back electro-motive force (EMF) or EMF voltage, back EMF constant, motor (including and usually, mainly due to winding) resistance and input voltage applied to the motor respectively.

Since the input electrical power is calculated as $$P_\text{in}=V_{in}I=I^2 R+V_E I=I^2 R+k_E \omega I$$ and the output electro-mechanical power is calculated as $$P_{out}=\tau\omega+I^2 R=k_\tau I\omega +I^2R\omega,$$ where the $I^R\omega$ in the previous equation represents the losses (as observed by the electro-mechanical output), we obtain $k_E=k_\tau$ from the equation $$P_{in}=I^2 R+V_E I=I^2 R+\tau\omega=P_{out}.$$

Why does back EMF tend to decrease as the rate of doing work increases. When load increases it reduces the angular speed of motor as a result induce current due to back emf also decreases because the flux changes at a slower rate than before.

Answer: From the analysis above, we can see that given a constant input voltage $V_{in}$, if the load $\tau$ increases then the speed $\omega$ decreases (in most cases), thus decreasing the back EMF $V_E$. The physical intuition is that the rate of change of the magnetic flux in the rotor windings of the motor decreases as $\omega$ decrease, thus causing the back EMF $V_E$ to decrease.
A: increasing power of motor is not same as increasing load on motor. 
if you increase the power of motor its back emf would increase as it will consume more energy.
V=IR
Increasing power of motor means decreasing its resistance and hence increasing current.
If you simply increase load on same motor its back emf would decrease as because of reason given by you.
Now,
V=IR
While you increase load, resistance of motor remalns same , so only current is reduced on increasing load , hence decreasing back emf.
